Controlled randomized porous structures and methods for making same

ABSTRACT

Improved randomized porous structures and methods of manufacturing such porous structures are disclosed. The scaffold of the porous structures are formed from by dividing the space between a plurality of spatial coordinates of a defined volume, where the plurality of spatial coordinates have been moved in a random direction and a random finite distance according to a predetermined randomization limit.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of pending U.S. patentapplication Ser. No. 16/728,668, filed Dec. 27, 2019, entitled“Controlled Randomized Porous Structures and Methods for Making Same”,which is a continuation application of pending U.S. patent applicationSer. No. 16/153,207, filed Oct. 5, 2018, entitled “Controlled RandomizedPorous Structures and Methods for Making Same”, which is a divisionalapplication of U.S. patent application Ser. No. 13/509,585, filed Aug.7, 2012, now U.S. Pat. No. 10,166,316, entitled “Controlled RandomizedPorous Structures and Methods for Making Same”, which application is thenational phase application under 35 U.S.C. 371 of InternationalApplication No. PCT/US2010/56602, filed Nov. 12, 2010, entitled“Controlled Randomized Porous Structures and Methods for Making Same”,which claims priority to, and the benefit, of U.S. Provisional PatentApplication No. 61/260,811, filed Nov. 12, 2009 and entitled “ControlledRandomization of Porous Structures for Medical Implants,” thedisclosures of which are incorporated by reference herein in theirentirety.

FIELD OF THE DISCLOSURE

The present invention generally relates to porous structures suitablefor medical implants, and more particularly to porous structuressuitable for medical implants that have improved combinations ofstrength, porosity and connectivity and methods for fabricating suchimproved porous structures.

BACKGROUND OF THE DISCLOSURE

Certain medical implants and orthopedic implants require strength forweight bearing purposes and porosity to encourage bone/tissue in-growth.For example, many orthopedic implants include porous sections thatprovide a scaffold structure to encourage bone in-growth during healingand a weight bearing section intended to render the patient ambulatorymore quickly. For example, metal foam structures are porous,three-dimensional structures that have been used in medical implants,particularly orthopedic implants, because they have the requisitestrength for weight bearing purposes as well as the requisite porosity.

Metal foam structures and other porous structures can be fabricated by avariety of methods. For example, one such method is mixing a powderedmetal with a pore-forming agent (PFA) and then pressing the mixture intothe desired shape. The PFA is removed using heat in a “burn out”process. The remaining metal skeleton may then be sintered to form aporous metal foam structure.

Another similar conventional method includes applying a binder topolyurethane foam, applying metal powder to the binder, burning out thepolyurethane foam and sintering the metal powder together to form a“green” part. Binder and metal powder are re-applied to the green partand the green part is re-sintered until the green part has the desiredstrut thickness and porosity. The green part is then machined to thefinal shape and re-sintered.

While metal foams formed by such conventional methods provide goodporosity, they may not provide the desired strength to serve as weightbearing structures in many medical implants. Further, the processes usedto form metal foams may lead to the formation of undesirable metalcompounds in the metal foams by the reaction between the metal and thePFA. Conventional metal foam fabrication processes also consumesubstantial amounts of energy and may produce noxious fumes.

Rapid manufacturing technologies (RMT) such as direct metal fabrication(DMF) and solid free-form fabrication (SFF) have recently been used toproduce metal foam used in medical implants or portions of medicalimplants. In general, RMT methods allow for structures to be built from3-D CAD models. For example, DMF techniques produce three-dimensionalstructures one layer at a time from a powder which is solidified byirradiating a layer of the powder with an energy source such as a laseror an electron beam. The powder is fused, melted or sintered, by theapplication of the energy source, which is directed in raster-scanfashion to selected portions of the powder layer. After fusing a patternin one power layer, an additional layer of powder is dispensed, and theprocess is repeated with fusion taking place between the layers, untilthe desired structure is complete.

Examples of metal powders reportedly used in such direct fabricationtechniques include two-phase metal powders of the copper-tin,copper-solder and bronze-nickel systems. The metal structures formed byDMF may be relatively dense, for example, having densities of 70% to 80%of a corresponding molded metal structure, or conversely, may berelatively porous, with porosities approaching 80% or more.

While DMF can be used to provide dense structures strong enough to serveas weight bearing structures in medical implants, the porous structuresconventionally used employ arrangements with uniform, non-random, andregular features that create weak areas where the struts of thethree-dimensional porous structure intersect. That is, the conventionalstructure configurations lack directional strength and compensate forthe weakness by making struts thicker, thereby decreasing the porosity,and conversely, a conventional structure with the desired porosity oftenlacks the desired strength because of the thinner struts. That is, thedesired strength can be achieved in the prior art at the expense ofporosity, or vice versa. There are no methods and/or products currentlyavailable that provide both the improved strength, improved porosity,and improved connectivity.

Further, trabecular bone structures are non-uniform and random inappearance on a micro-scale. It is also known that effective medicalimplants must be physiologically compatible with their surroundings inaddition to providing the requisite strength, porosity and connectivity.Yet the conventional porous structures with uniform, non-random, andregular features that do not resemble trabecular bone structures. Forexample, U.S. Publication Nos. 2006/0147332 and 2010/0010638 showexamples of these prior art configurations employed to form porousstructures that exhibit the disadvantages discussed above, e.g., weakareas at the strut intersections, improved strength at the expense ofporosity, and no trabecular features.

One way to enhance the effectiveness of an orthopedic implant may be torandomize the porous structure of an implant so it better simulatestrabecular structures in which it is implanted. Therefore, in additionto strength, porosity and connectivity properties, it is believed thatthe performance of an implant with a porous structure could be improvedif the porous structure could be randomized porous thereby providing arandomized scaffold structure as opposed to a uniform open cellstructure. Methods known in the art to create randomized structurestypically involve randomizing an existing uniform structure. Thesemethods, however, are limited because they typically require manualmanipulation of the struts, i.e., solid space, of one unit to match upwith another unit to build a scaffold of desired dimensions. If thestruts of the units do not match up, the integrity of the structure maybe compromised if it has too many loose struts. Similarly, a randomizedstructure with poorly oriented struts may have poor distribution ofresidual stresses due to the manufacturing method resulting in warped orinaccurate parts. Accordingly, the structure of the initial units of theprior art, either identical or not, is usually simple to keep thestacking or building process manageable. Otherwise, building a scaffoldfrom complex randomized initial units would be too time consuming andcostly, particularly in computation expenses. Further, an additionaldrawback to randomizing an existing uniform structure is potentiallymaking the structure weaker due to the unanticipated changes in theproperties of the structure resulting from changes in the modulus anddirection during the randomization process. Consequently, an originalrandomized structure, as opposed to a randomized existing structure,provides for improved strength along with improved porosity and enhancedcomplexity—e.g., trabecular features. As mentioned above, in the priorart, software applications typically produce porous structures that arepredominantly uniform and regular. For efficiency, they repeat a smallunit tile in the coordinate directions to fill a volume without gapsbetween the tiles. However, relatively few and simple shapes areemployed within the unit tile due to the complexity of matching thesetiles together.

Further, as a result of the deficiencies of metal foam implants andimplants fabricated using conventional DMF methods, some medicalimplants require multiple structures, each designed for one or moredifferent purposes. For example, because some medical implants requireboth a porous structure to promote bone and tissue in-growth and aweight bearing structure, a porous plug may be placed in a recess of asolid structure and the two structures may then be joined by sintering.Obviously, using a single structure would be preferable to using twodistinct structures and sintering them together.

In light of the above, there is still a need for efficient methods tomanufacture three dimensional porous structures, and the structuresthemselves, with randomized scaffold structures that provide forimproved porosity without sacrificing the strength, improved strengthincluding seamless junctions between units, and improved connectivityand having trabecular features.

SUMMARY OF THE DISCLOSURE

One objective of the invention is to provide porous biocompatiblestructures suitable for use as medical implants that have improvedstrength for weight bearing purposes and porosity for tissue in-growthstructures.

Another objective of the invention is to provide porous biocompatiblestructures suitable for use as medical implants that have improvedconnectivity to resemble trabecular bone features.

Another objective of the invention is to provide porous biocompatiblestructures that promote bone tissue and soft tissue in-growth.

Another objective of the invention is to provide porous biocompatiblestructures suitable for use as medical implants having a controlled, yetrandom arrangement of struts and nodes for improved performancecharacteristics.

Yet another objective of the invention is to provide methods forfabricating such improved porous biocompatible structures.

Another objective of the invention is to provide efficient methods forfabricating randomized porous structures by manipulating the spacebetween the struts.

Yet another objective of the invention is to provide methods forproviding a seamless fit between structures that are joined together,regardless of whether the structures are identical or not.

Another objective of the invention is to provide methods to fabricate arandomized porous structure that can be customized to specific needs,e.g., a particular patient or application, having the appropriatedistribution, pore size, porosity, and strength.

Another objective of the invention is to provide methods for controllingthe randomization of a scaffold for a structure.

To meet the above objectives, there is provided, in accordance with oneaspect of the invention, a method for fabricating a porous structurecomprising the steps of: creating a model of a porous structure, thecreating step includes defining a three dimensional space having anouter boundary and an inner volume, placing a plurality of outer spatialcoordinates along the boundary, placing a plurality of inner spatialcoordinates in the inner volume, moving one or more inner spatialcoordinates a finite distance in a random direction, moving one or moreouter spatial coordinates a finite distance in a random direction. Thestep of creating a model of a porous structure further includes dividingthe volume of the three dimensional space evenly among the randomizedouter and inner spatial coordinates, defining the boundary of one ormore divided volume with one or more struts and one or more nodes, whereeach strut has a first end, a second end, and a continuous elongatedbody between the first and second ends for each strut, and each node isan intersection of at least two struts, and selecting a thickness and ashape for one or more struts. The method further includes the step offabricating the porous structure according to the model by exposingfusible material to an energy source.

In accordance with another aspect of the invention, the method alsoincludes a step of providing a second three dimensional space that is aduplicate of the first three dimensional space where the inner and outercoordinates have already been randomized.

In one embodiment, the moving of the inner spatial coordinates a finitedistance in a random direction is performed within a preselected orpredetermined randomization limit that avoids any overlap of the innerspatial coordinates. In another embodiment, the moving of the outerspatial coordinates a finite distance in a random direction is performedwithin a predetermined randomization limit so that the randomized outerspatial coordinates of one three dimensional space match or correspondto their respective outer spatial coordinates on a second substantiallyidentical three dimensional space. Alternatively, the second threedimensional space is not substantially identical to the first threedimensional space.

In one embodiment, a Voronoi tessellation is applied to the randomizedspatial coordinates and struts to remove redundant struts. In anotherembodiment, the method includes the step of fabricating the porousstructure that comprises two or more substantially identical threedimensional spaces having randomized spatial coordinates andcorresponding struts. In some embodiments where the overlap of inner andouter spatial coordinates after randomization or perturbation is notproblematic, randomization limits may be avoided altogether or usedsparingly.

In some embodiments, only selected inner and/or outer spatialcoordinates are perturbed or randomized. In other embodiments all orsubstantially all inner and/or outer spatial coordinates are randomizedor perturbed.

The perturbations or randomizations may be carried out for each innerand each outer spatial coordinate, or for some of the outer spatialcoordinates and some of the inner spatial coordinates, or for some ofthe outer spatial coordinates and none of the inner spatial coordinates,or a little as one region of the outer spatial coordinates. A completerandomization of all spatial coordinates is not required.

In some embodiments, the predetermined randomization is configured toavoid at least one inner spatial coordinate from overlapping with atleast one other inner spatial coordinate. In other embodiments, themethod further includes selecting a predetermined randomization limitfor at least one inner spatial coordinate, the selecting comprising thesteps of: defining a volume around the at least one inner spatialcoordinate, the volume is based at least on the proximity of one othersurrounding inner spatial coordinate; and limiting the randomizedmovement of the at least one inner spatial coordinate to be within thedefined volume.

Yet in other embodiments, the defined volume comprises a geometric shapeselected from the group consisting of spheres, Archimedean shapes,Platonic shapes, polyhedrons, prisms, anti-prisms and combinationsthereof. In some embodiments, at least one dimension of said definedvolume has a radius of less than 50% the distance between said at leastone inner spatial coordinate and other surrounding inner spatialcoordinate.

In other embodiments, the matching is accomplished by moving at leasttwo corresponding outer spatial coordinates the same finite distance andthe same direction. In some embodiments, the three dimensional spacecomprises a geometric shape selected from a group consisting of spacefilling polyhedra, space-filling convex polyhedra with regular faces,and space-filling convex polyhedra with irregular faces.

Yet in other embodiments, the shape selected for the struts comprises apolygon. In some refinements, the shape selected for one strut differsfrom the shape of another strut, where the selected shape is configuredto promote tissue ingrowth.

In some embodiments, the fabricating step further comprises selecting amaterial for fabricating the one or more struts from the groupconsisting of metal, ceramic, metal-ceramic (cermet), glass,glass-ceramic, polymer, composite and combinations thereof. In otherembodiments, the method further comprises selecting a metallic materialfrom the group consisting of titanium, titanium alloy, zirconium,zirconium alloy, niobium, niobium alloy, tantalum, tantalum alloy,nickel-chromium (e.g., stainless steel), cobalt-chromium alloy andcombinations thereof.

According to another aspect of the invention, there is provided a porousstructure comprising a plurality of struts, each strut comprises: afirst end; a second end; and a continuous elongated body between saidfirst and second ends, said body having a thickness and a length; and aplurality of nodes, each node comprises an intersection of at least twostruts, where the plurality of struts and nodes formed from a modelcreated by dividing the space between a plurality of spatial coordinatesof a defined volume, said plurality of spatial coordinates having beenmoved in a random direction and a random finite distance according to apredetermined randomization limit.

In some embodiments, the predetermined randomization is configured toavoid at least one inner spatial coordinate from overlapping with atleast one other inner spatial coordinate. In other embodiments, thedimension of said defined space surrounding said one or more spatialcoordinates is based at least on the proximity of one other surroundingspatial coordinate. In some refinements, the other spatial coordinate isa nearest neighbor to the one or more spatial coordinates.

Yet in other embodiments, the defined space comprises a geometric shapeselected from the group consisting of spheres, Archimedean shapes,Platonic shapes, polyhedrons, prisms, anti-prisms and combinationsthereof. In other refinements, at least one dimension of said definedvolume has a radius of less than 50% the distance between said one ormore spatial coordinates and said one other surrounding spatialcoordinate.

In some refinements, the three dimensional space comprises a geometricshape selected from a group consisting of space filling polyhedra,space-filling convex polyhedra with regular faces, and space-fillingconvex polyhedra with irregular faces.

In other embodiments, a Voronoi tessellation is applied to therandomized plurality of spatial coordinates to divide the space betweenall spatial coordinates. In some refinements, the shape for the crosssectional of said struts comprises a polygon. In some refinements, theshape selected for one strut differs from the shape of another strut,where the shape selected is configured to promote tissue ingrowth.

In some embodiments, the porous structure further includes a materialselected from the group consisting of metal, ceramic, metal-ceramic(cermet), glass, glass-ceramic, polymer, composite and combinationsthereof. In other refinements, the metallic material is selected fromthe group consisting of titanium, titanium alloy, zirconium, zirconiumalloy, niobium, niobium alloy, tantalum, tantalum alloy, nickel-chromium(e.g., stainless steel), cobalt-chromium alloy and combinations thereof.

According to yet another aspect of the present invention, there isprovided, a method for providing a seamless union between at least twoscaffolds comprising the steps of: providing at least twothree-dimensional spaces, each space having an outer boundary and aninner volume, providing a total volume having said at least two spaces;placing a plurality of spatial coordinates along the outer boundary ofeach of said three-dimensional space, placing a plurality of innerspatial coordinates in the inner volume, of each of saidthree-dimensional space; forming said scaffold by dividing the volume ofthe three dimensional space among the outer and inner spatialcoordinates and defining the boundary of a portion of said dividedvolume with one or more struts, where each strut has a first end, asecond end, and a continuous elongated body between the first and secondends for each strut, selecting at least one thickness and at least oneshape for one or more struts; and fabricating a porous structureaccording to the scaffold with said one or more struts having at leastone thickness and at least one shape by exposing fusible material to anenergy source. In some embodiments, the method further includes movingat least one spatial coordinate from one of said plurality of outerspatial coordinates and said plurality of inner spatial coordinates;said movement configured to provide a scaffold having a seamless unionbetween said at least two spaces.

According to yet another aspect of the invention, there is provided, aporous structure having a plurality of struts, each strut comprises: afirst end; a second end; and a continuous elongated body between saidfirst and second ends, said body having a thickness and a length; and aplurality of nodes, each node comprises an intersection of at least twostruts, where the plurality of struts and nodes formed from a modelcreated by dividing the space between a plurality of spatial coordinatesof two or more defined volumes. In some embodiments, a Voronoitessellation is applied to the spatial coordinates to divide the space.

Other advantages and features will be apparent from the followingdetailed description when read in conjunction with the attacheddrawings. The foregoing has outlined rather broadly the features andtechnical advantages of the present invention in order that the detaileddescription of the invention that follows may be better understood.Additional features and advantages of the invention will be describedhereinafter which form the subject of the claims of the invention. Itshould be appreciated by those skilled in the art that the conceptionand specific embodiment disclosed may be readily utilized as a basis formodifying or designing other structures for carrying out the samepurposes of the present invention. It should also be realized by thoseskilled in the art that such equivalent constructions do not depart fromthe spirit and scope of the invention as set forth in the appendedclaims. The novel features which are believed to be characteristic ofthe invention, both as to its organization and method of operation,together with further objects and advantages will be better understoodfrom the following description when considered in connection with theaccompanying figures. It is to be expressly understood, however, thateach of the figures is provided for the purpose of illustration anddescription only and is not intended as a definition of the limits ofthe present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the disclosed methods andapparatuses, reference should be made to the embodiments illustrated ingreater detail in the accompanying drawings, wherein:

FIG. 1 is a perspective view of the initial cube volume illustrating aportion of the outer seed points or outer spatial coordinates accordingto one aspect of the present invention;

FIG. 2 is a perspective view of the initial cube volume of FIG. 1 withinner seed points according to one aspect of the present invention;

FIG. 3 is a perspective view illustrating a randomization of the innerseed points or spatial coordinates according to one aspect of thepresent invention;

FIG. 4 is a perspective view illustrating one embodiment to confirmcompatibility of the inner seed points according to one aspect of thepresent invention;

FIGS. 5A-5B are perspective views illustrating one embodiment torandomize certain outer seed points according to one aspect of thepresent invention;

FIGS. 6A-6B are perspective views illustrating one embodiment torandomize other outer seed points according to one aspect of the presentinvention;

FIGS. 7A-7B are perspective views illustrating one embodiment torandomize yet other outer seed points according to one aspect of thepresent invention;

FIG. 8 illustrates one embodiment of a seed point cloud volume definedby randomized inner seed points and randomized outer seed pointsaccording to one aspect of the present invention;

FIG. 9 illustrates one embodiment of an array of seven of the seed pointcloud tiles illustrated in FIG. 8 according to one aspect of the presentinvention;

FIG. 10 illustrates one embodiment of a web or scaffold of randomizedstruts produced according to one embodiment of the present invention;

FIG. 11 illustrates the web or scaffold of randomized struts of FIG. 10placed as the center tile in an array according to one aspect of thepresent invention;

FIG. 12 illustrates the various lines of a convex hull according to oneaspect of the present invention;

FIG. 13 illustrates one embodiment to remove certain redundant linesfrom the convex hull of FIG. 12 according to one aspect of the presentinvention;

FIGS. 14-15 illustrate the seamless joining of two identical volumes ofrandomized struts disposed side-by-side according to one aspect of thepresent invention;

FIG. 16 illustrates one refinement to apply certain shapes andthicknesses to the struts of the volume of randomized struts in FIG. 11;

FIG. 17 illustrates one embodiment of a porous structure with four (4)volumes of randomized struts having a 10% randomization limit accordingto one aspect of the present invention;

FIG. 18 illustrates one embodiment of a porous structure with four (4)volumes of randomized struts having a 20% randomization limit accordingto one aspect of the present invention;

FIG. 19 illustrates one embodiment of a porous structure with four (4)volumes of randomized struts having a 30% randomization limit accordingto one aspect of the present invention;

FIG. 20 is a partial view of the porous structure of FIG. 19illustrating one embodiment of a porous structure having a seamlessinterface between two or more volumes of randomized struts according toone aspect of the present invention;

FIG. 21 is a scanning electron microscope (SEM) image of a stainlesssteel random porous structure made in accordance with one aspect thepresent invention (image taken at 50×);

FIG. 22 is another SEM image of a stainless steel random porousstructure made in accordance with one aspect the present invention(image taken at 50×);

FIGS. 23-25 are photographs of structures fabricated on an EOS™ metallaser sintering machine, employing a 30% randomization limit inaccordance with one aspect of the present invention;

FIGS. 26A-26C illustrates one embodiment of a porous coating beingformed from volumes of randomized struts according to one aspect of thepresent invention;

FIG. 27 illustrates one embodiment of a Boolean intersect volumeaccording to one aspect of the present invention.

FIGS. 28A-28B illustrate a porous structure according to one aspect ofthe present invention with two different randomized tiles seamlesslyjoined together.

It should be understood that the drawings are not necessarily to scaleand that the disclosed embodiments are sometimes illustrateddiagrammatically and in partial views. In certain instances, detailswhich are not necessary for an understanding of the disclosed methodsand apparatuses or which render other details difficult to perceive mayhave been omitted. It should be understood, of course, that thisdisclosure is not limited to the particular embodiments illustratedherein.

DETAILED DESCRIPTION

The present disclosure provides for methods to fabricate porousstructures with improved strength, porosity, and connectivity.Preferably, the improved porous structures of the present invention isformed by using a free-from fabrication method, including rapidmanufacturing techniques (RMT) such as direct metal fabrication (DMF).Typically, in RMT or free-form fabrication, a model, or calculationsdefining the desired structure, or a computer readable file of thedesired structure is provided to a computer-aided machine or apparatusthat has an energy source such as a laser beam to melt or sinter powderto build the structure one layer at a time according to the providedmodel.

For example, RMT is an additive fabrication technique for manufacturingobjects by sequential delivering energy and/or material to specifiedpoints in space to produce that part. Particularly, the objects can beproduced in a layer-wise fashion from laser-fusible powders that aredispensed one layer at a time. The powder is fused, melted, remelted, orsintered, by application of the laser energy that is directed inraster-scan fashion to portions of the powder layer corresponding to across section of the object. After fusing the powder on one particularlayer, an additional layer of powder is dispensed, and the process isrepeated until the object is completed.

Detailed descriptions of selective laser sintering technology may befound in U.S. Pat. Nos. 4,863,538; 5,017,753; 5,076,869; and 4,944,817,the disclosures of which are incorporated by reference herein in theirentirety. Current practice is to control the manufacturing process bycomputer using a mathematical model created with the aid of a computer.Consequently, RMT such as selective laser re-melting and sinteringtechnologies have enabled the direct manufacture of solid or 3-Dstructures of high resolution and dimensional accuracy from a variety ofmaterials.

In one embodiment of the present invention, the porous structure isformed from powder that is selected from the group consisting of metal,ceramic, metal-ceramic (cermet), glass, glass-ceramic, polymer,composite and combinations thereof. In another embodiment, metallicpowder is used and is selected from the group consisting of titanium,titanium alloy, zirconium, zirconium alloy, niobium, niobium alloy,tantalum, tantalum alloy, nickel-chromium (e.g., stainless steel),cobalt-chromium alloy and combinations thereof.

In another embodiment, the disclosed fabrication methods may form acomplete orthopedic implant structure, or the disclosed techniques maybe applied to a substrate or work piece which forms part of an implant.The fabrication methods disclosed herein produce porous structures thedesired porosity, pore size, strength and connectivity by controllingthe randomization of the scaffold of a porous structure. Cellattachment, bone in-growth and initial fixation may be improved with therandomized scaffold structures produced by the disclosed methods becausethe scaffold structures better simulate natural trabecular structures.As an added benefit, the implants are more aesthetically pleasing to thephysician and patient, since they better resemble natural trabecularstructures.

Preferably, the randomized scaffold can be created by dividing a definedvolume evenly between a series of seed points that have been randomizedat the boundary and within the volume. The seed points have beenrandomized according to a predetermined randomization limit that ispreferably designed to avoid any overlap of the seed points within thevolume. If more than one identical volume is used to create therandomized scaffold, the predetermined randomization limit can be usedto ensure the seed points at the boundary of the volume (“outer seedpoints”) match up with the outer seed points of other identical volumes.As described, the volume has been divided into random portions becausethe seed points have been randomly placed, but the random division iscontrolled because there was a limit on the random placement of the seedpoints. The border of the divided portions serve as the struts of therandomized scaffold, and the randomized scaffold can be built into aporous structure once a strut thickness and shape are selected.

The following paragraphs provide more detailed descriptions and variousembodiments and refinements of the present invention. Referring to FIGS.1 and 2, an initial geometry in the form of a cube 100 may be chosen,which defines a volume. The cube 100 has an outer boundary 102 and aninner or interior volume 104. For demonstration purposes, FIG. 2represents inner volume 104 as a cube within cube 100. This is not meantto limit the scope of the present disclosure where inner volume 104 canbe any space within the outer boundary 102. In other embodiments, it isenvisioned that other space-filling polyhedra can be used to define thedisclosed volume. As illustrated, a plurality of outer seed points 106,108, and 110 are placed at the outer boundary 102 of cube 100. WhileFIG. 1 shows only the top face of cube 100 containing these outer seedpoints, it is envisioned that in other embodiments, all or most of thefaces of the cube or other space-filling polyhedra may contain theseouter seed points. In FIG. 1, there are three types of outer seedpoints. The first type is the corner outer seed points 106, the secondtype is the edge outer seed points 108, and the third is the inboundouter seed points 110. In FIG. 1, These outer seed points are evenlydistributed at the boundary of cube 100. Referring to FIG. 2, inaddition to these outer seed points, a plurality of inner seed points112 are placed in the inner volume 104. The number of seed points andtheir initial positions illustrated in these FIGS. is intended forillustration purposes only, and the actual number of inner and outerseed points depends on the initial spatial geometry and desiredrandomness. Also, in the preferred embodiment, the inner seed points areindexed and randomized independently of the indexing and randomizationof the “outer” seed points. In other refinements, the randomization ofthe inner and outer seed points are not independent. For more complexinner seed point tiles or volumes, the copying or arraying processillustrated in FIG. 4 may need to be expanded beyond the seven-tilearray shown in FIG. 4. Also, in some embodiments, the inner and outerseed points may be defined based at least upon the particular seedpoint's level of influence on the boundary between volumes. Forinstance, seed points that do not have any or have minimal influence onthe boundary between volumes would be defined as inner seed points. Onthe other hand, seed points that have substantial influence on theboundary would be defined as outer seed points. Further, in theseembodiments, it may not be necessary to array the inner seed point tilesor volumes as the inner seed points, as defined, should not have anyinfluence or minimally influence the boundary.

After the inner seed points 112 are placed or created, their positionsare randomized in three-dimensional space as illustrated in FIG. 3. Eachseed point or spatial coordinate 112 is moved or “perturbed” in randomdirections by random magnitudes using a random number generatoralgorithm. That is, each seed point or spatial coordinate 112 is moved afinite distance in a random direction within cube 100, where the finitedistance each seed point has been moved is also random. The perturbationor moving of the seed points 112 is not completely random, however,because a preselected or predetermined randomization limit is imposed onthe random movement of each seed point 112.

In one embodiment, the predetermined randomization limit is based uponthe position of the closest neighboring seed point 112, which can bedetermined by, for instance, the nearest neighbor algorithm or othersimilar algorithms. The limit ensures that the random movements of theinner seed points 112 do not cause one inner seed point to overlap withanother inner seed point 112. One seed point can overlap another seedpoint by partially or fully lying on top of the other seed point, orthere can also be overlap when one seed point enters the defined volumesurrounding another seed point. Typically, overlapping occurs more ormost frequently when two dissimilar tiles are joined together becausethe more dissimilar the tiles, the more difficult it is to distinguishinner and outer seed points. Conversely, overlapping occurs lessfrequently when substantially similar tiles are combined. One way ofensuring no overlap is to limit the movement of any inner seed point 112to be within a volume determined by the proximity of surrounding innerseed points 112. In one embodiment, such a volume may be defined as ahexahedron or a sphere with at least one of its dimensions having aradius of less than 50% or half the distance to the closest neighboringseed point. For example, referring to FIG. 2, using the inner seed point112 a located at the lower left corner of the inner volume 104 as anexample, the closest neighboring seed points to inner seed point 112 aare inner seed points 112 b and 112 c. If the randomization of the innerseed point 112 a is limited in magnitude or distance to within thevolume of the sphere 114 surrounding point 112 a, then the randomplacement of inner seed point 112 a can only occur within that volume114 and any random movements of point 112 a cannot result in an overlapof point 112 a with the other two seed points 112 b and 112 c.

In other embodiments, more abstract and complex volumes may be definedto delineate the bounds of perturbation for a given seed point. In yetother embodiments, different volume sizes can be used to limit therandomization. For instance, a 10% randomization limit placed on themovements of the inner seed points 112 means that each seed point 112can be moved randomly within a sphere (or other shapes) having a radiusof 10% of the distance between that particular seed point and itsclosest neighboring seed point prior to the perturbation. A 30%randomization limit means that each seed point can be moved randomlywithin a sphere having a radius of 30% of the distance between the seedpoint and its closest neighbor prior to perturbation. Accordingly, bylimiting the random magnitude and direction of the perturbation of eachinner seed point 112 to within a sphere or other defined threedimensional space 114 with a radius of less than half the distance to aneighboring seed point, the two seed points 112 a and 112 c cannot notoverlap or engage each other even if the randomization results in theseseed points moving directly toward each other. In some embodiments,greater limits of randomization may be established in order to allowseed point overlaps and seed point crossings during perturbation steps.However, by preventing seed points from overlapping and/or crossing, ahigher level of porosity control and strength may be achieved.Accordingly, the randomization limit can be any number between 0% to100% of the distance between a particular seed point and its closestneighbor, e.g., 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%, 55%,60%, 65%, 70%, 75%, 80%, 85%, 90%, 95%, or 100%. In other embodiments,the range can exceed 100% the distance between a particular seed pointand its closest neighbor. For instance, the range of the randomizationlimit can be 100% to 200% or 0% to 200%. Although the specification hasdiscussed defining the predetermined randomization limit with respect toinner spatial coordinates, it should be understood that the stepsdiscussed above can apply equally to randomizing outer spatialcoordinates. In further embodiments, inner and outer seed points may berandomized using different methods and degrees of randomization.

In the preferred embodiment, the model or randomized scaffold of theporous structure is created by arraying or stacking identical cloudvolumes or tiles of perturbed seed points. When the duplicated cloudvolumes or tiles are arrayed or stacked, it is preferred that therandomized inner seed points 112 do not intercept or create conflictswith the outer seed points 106, 108, and 110. One way of ensuringcompatibility between the inner and outer seed points is to arrayidentical versions of cube 100 with perturbed inner seed points 112 inthree-dimensional space as illustrated in FIG. 4 where one of the sixidentical versions of cube 100 of FIG. 3 is placed adjacent to each faceof cube 100 of FIG. 3.

In a refinement, inner seed points 112 are randomized before the outerseed points 106, 108, and 110. Turning to FIGS. 5A-7A, the outer seedpoints 106, 108, and 110 are shown prior to perturbation. That is, FIG.5A shows inbound outer seed points 110 evenly distributed on the topface, front face, and right side face of cube 100. FIG. 6A shows theedge outer seed points 108 evenly distributed around the edges of thetop face, front face, and right side face of cube 100. FIG. 7A shows thecorner outer seed points 106 evenly placed at the corners of the topface, front face, and right side face of cube 100. For simplificationpurposes, the outer seed points 106, 108, and 110 are shown only for thetop face, front face, and right side face of cube 100. In otherembodiments, more or less faces of the initial cube or otherspace-filling polyhedra can include these outer seed points. In thepreferred embodiment, instead of randomizing the outer seed points 106,108, and 110 together or as a group like the inner seed points 112, theouter seed points 106, 108, and 110 are randomized essentially in pairsdue to the six-sided cubical geometry of cube 100. That is, each outerseed point and its counterpart outer seed points are identified andrandomized in the same direction and magnitude.

Turning to FIGS. 5A and 5B, the outer seed points 110 a of a front faceregion 118 are first identified and indexed. All the front outer seedpoints 110 a may be randomized at the same time using the random numbergenerator algorithm to generate the random finite distance and directionfor each front outer seed point 110 a, while the predeterminedrandomization limit (e.g., a sphere at 30% limit). Because the initialgeometry 100 is a regular hexahedron, a corresponding set of outer seedpoints (not shown) on a back face region 120 are also identified,indexed, and randomized. Each back outer seed point (not shown) israndomized in the same direction and magnitude (distance) as itscorresponding front outer seed point 110 a. In other words, each frontouter seed points 110 a has identical x- and z-coordinates as its andits corresponding back outer seed point, but both have differenty-coordinates. Each of the back outer seed points may be randomizedindividually or all the back outer seed points may be randomized as agroup, so long as the randomization used for each back outer seed pointis of the same magnitude and direction as its corresponding front outerseed point 110 a. This process results in the front region 118 and theback face region 120 with identical randomized inbound outer seedpoints. The result is shown in FIG. 8, where the inbound outer seedpoints 110 a of face 122 are identical in the x-direction andz-direction as the inbound outer seed points 110 b of face 124. Toconfirm compatibility, the point clouds shown in FIG. 5B may be copiedin three-dimensional space upwards, downwards and to all four sides in asimilar manner as shown in FIG. 4.

For purposes of keeping FIGS. 5A and 5B simplified, the inbound outerseed points 110 on the top and side faces of cube 100 are not perturbed.Also, referring to FIG. 8, the faces, other than faces 122 and 124, ofcube 100 are intentionally left blank. This, however, is only fordemonstration purposes and does not limit the scope of either the claimsor the present disclosure. That is, it is understood that the side outerseed points 110 c can also be identified, indexed, and randomized asdescribed for front face 118 and back face 120. That is the right sideouter seed points 110 c can be perturbed first according to a randomnumber generator algorithm and a predetermined randomization limit, asdescribed above. A corresponding set of left side outer seed points (notshown) are then randomized individually or as a group, where themagnitude and direction of each perturbation of the right outer seedpoints are identified and applied to each corresponding left outer seedpoints (not shown). Accordingly, the right and left outer seed pointswill have identical y- and z-coordinates, and different x-coordinates,after perturbation. To confirm compatibility, the resulting point cloudscan be copied in three-dimensional space upwards, downwards and to allfour sides in a similar manner as shown in FIG. 4. The same process canbe performed for the top outer seed points 110 d and correspondingbottom outer seed points. That is, after the top 110 d and correspondingbottom outer seed points are identified, the corresponding pair of outerseed points are randomized using the same directions and magnitude toprovide top and bottom outer seed points with identical x- andy-coordinates but different z-coordinates. The result is that theopposing top and bottom faces with identically randomized seed pointclouds. To confirm compatibility, the resulting point clouds shown arecopied in 3D space upwards, downwards and to all four sides in a similarmanner as shown in FIG. 4.

In summary, inbound outer seed points disposed on, adjacent to, ordefining a face region like seed points 110 a, c, d in FIG. 5A, may berandomized as a group similar to the inner seed points 112; however,inbound outer seed points disposed along an opposite face region need tobe moved in an identical fashion to their counterparts as shown anddescribed above. In the embodiment shown in 5B, at least two of the sixface regions will have matching inbound outer seed point patterns inspace. In some embodiments, at least some seed points may be randomized,while other seed points remain unperturbed. For instance, somerefinements may exist, where perturbations only occur at every Nth seedpoint in a region. Other refinements may include cubes or tiles orvolumes of perturbed seed points, e.g., cube 800 of FIG. 8, where theone or more inner seed points 112 are perturbed while one or more outerseed points 106, 108, and 110 remain unperturbed and arranged in anordered fashion to ensure compatibility between either randomized ornon-randomized cubes or tiles or volumes.

It may be preferable to provide a gradient of randomness while stillmaintaining a controlled porosity and/or pore size. The gradient ofrandomness can be achieved by many means. One way is to gradually orabruptly increase the randomization limit (e.g., increasing from 10% to30% limit) in one or more directions within a given cube or tile orvolume. Another way is to gradually or abruptly increase the number ofperturbed seed point in one or more directions within a cube or tile orvolume. In yet other embodiments, only one or more outer seed pointregions may be perturbed, and inner seed points 65 remain unperturbed toform a sandwich of non-random seed points between random seed points.More alternatively, some refinements may exist where seed points areonly perturbed at predetermined regions within an overall seed pointcloud cube or tile or volume, e.g., cube 800 of FIG. 8. Variouscombinations of the aforementioned embodiments are can be employed.

Turning to FIGS. 6A and 6B, a similar randomization process is employedfor the edge outer seed points 108 disposed along the edge regions ofcube 100. With embodiments employing regular hexahedron geometry (cube)as illustrated, seed points edge outer seed points 108 may be randomizedin groups according to the following disclosure. FIG. 6A illustrates aneven distribution of the edge outer seed points 108, which are disposedalong the edge regions parallel with the x-axis, y-axis, and z-axis. Inthe preferred embodiment, all the edge outer seed points 108 areidentified and randomized together as a group or individually.Regardless of individual or group randomization, the edge outer seedpoints 108 are perturbed with identical directions and magnitudes asshown in FIG. 6B. For purposes of keeping FIGS. 6A and 6B simplified,the edge outer seed points 108 of the back, bottom, and left faces ofcube 100 are not shown, and only selected edge outer seed points 108 areperturbed. This, however, is only for demonstration purposes and doesnot limit the scope of either the claims or the present disclosure. Toconfirm compatibility, the point clouds shown in FIG. 6B can be copiedin 3-D space upwards, downwards and to all four sides in a similarmanner as shown in FIG. 4. In confirming compatibility, it is preferredthat duplicated seed points are removed. In other embodiments, however,duplicated seed points may not be removed. In another embodiment,compatible seed point clouds may be reduced prior to any copying and/orarraying to prevent duplicate seed points during the multiplicationprocess.

The perturbation process can be similarly repeated for other edge outerseed points 108. That is, other edge outer seed points 108 can also beidentified, indexed, and randomized according to a random numbergenerator algorithm and a predetermined randomization limit, asdescribed above. A corresponding set of edge outer seed points (notshown) located at the opposite face of the cube is then randomizedindividually or as a group, where the magnitude and direction of eachperturbation of the corresponding set of points are identical to thepreviously randomized set. Thus, for edge outer seed points 108 disposedalong an edge region that is parallel to an axis, the seed points thatshare a common coordinate value for that axis can be randomizedindependently within the group or together, as long as their counterparts are randomized identically to ensure compatible edge regions.Here, unlike FIGS. 5A and 5B, perturbation of one edge outer seed point108 a results in the perturbation of three other corresponding edgeouter seed points 108 b (the third edge outer seed point is not shown).This is because two adjacent sides share one edge outer seed point 108.FIG. 8 demonstrates the identical randomization of corresponding sets ofedge outer seed points 108 on faces 122 and 124. The other faces areleft intentionally blank to keep FIG. 8 simplified. This, however, isnot intended to limit the scope of the claims or present disclosure. Itis envisioned that other edge seed points can be perturbed in the samemanner and included in cube 800.

Turning to FIGS. 7A and 7B, for regular hexahedron geometry, the cornerouter seed points 106 are identified and may be randomized together as agroup but in an identical fashion as shown in FIG. 7B. In other words,each corner seed point 106 is moved in the same direction and by thesame magnitude to ensure that all eight corner regions are compatible asillustrated in FIG. 7B. To confirm compatibility, the corner pointclouds shown in FIG. 8A are copied in 3D space upwards, downwards and toall four sides in a similar manner as shown in FIG. 4.

FIG. 8 demonstrates a resulting overall seed point cloud cube or volume800 having an inner seed point cloud volume 104, and identical outerseed point clouds at face region 122 and face region 124, includingidentical edge, inbound, and corner outer points 106, 108, and 110. Asmentioned above, only two faces of cube 800 are shown, but that is onlyfor demonstration purposes and is not intended to limit the scope of theclaims or the present disclosure. As already discussed, to ensurecompatibility between the cubes, the seed point cloud volume 800 may becopied in three-dimensional space to the front, back, top, bottom andboth sides to produce array 900 as illustrated in FIG. 9. To keep FIG. 9simplified, inner seed point cloud volume 104 has been omitted. This,however, is not intended to limit the scope of the claims or the presentdisclosure.

In summary, after or during perturbation of the inner and outer seedpoints, to ensure that no unexpected aberrations occur at the boundariesor faces between the seed point cloud cubes or tiles or volumes, therandomized seed point cloud cube or tile or volume may be arrayed withidentical seed point cloud tiles to make sure that: (1) the front andback face regions have matching seed point spatial patterns; (2) theright and left or side face regions have matching seed point spatialpatterns; (3) the top and bottom face regions have matching seed pointspatial patterns; (4) the edge regions disposed along and parallel tothe x-axis have matching seed point spatial patterns; (5) the edgeregions disposed along and parallel to the y-axis have matching seedpoint spatial patterns; (6) edge regions along and parallel to thez-axis have matching seed point spatial patterns; and (7) all cornerregions have matching seed point spatial patterns. In one embodiment, anarray of seed point cloud volume may be used for further processing tocreate the randomized scaffold of the porous structure. It should benoted that edge regions may not be parallel to a particular axis,especially for more complex shapes used for the initial geometry.

In a refinement, the randomization of the inner seed points 112 and theouter seed points 106,108, and 110 of the base cube or tile or volume isperformed using a numerical computing environment algorithm. Forexample, the numerical computing environment algorithm may be a MATLAB™algorithm. Other non-limiting examples of numerical computingenvironment programs SCILAB™, OCTAVE™, FREEMAT™, JMATHLIB™, MATHNIUM™,TELA™, ALGAE™, LUSH™, YORICK™, RLAB™, MAXIMA™, SAGE™, EULER™, S-LANGLIBRARY™, PYTHON™, NUMPY™, SCIPY™, THE R PROJECT′, LUA™, any similarprograms that provide the same or similar computing environments as thelisted programs, and combinations, sub-combinations and variationsthereof. Other programs will be apparent to those skilled in the art andfuture programs either under current development or future developmentwill also be apparent to those skilled in the art. This disclosure isnot limited to the particular software used to generate the randomizedbase tile and the software used to create three-dimensional structuresfrom the multiplied randomized base cube or tile or volume. The volumeof the initial geometry and number of seed points distributed within thevolume and at the boundary can be chosen at the user's discretion. Inthe preferred embodiment, the volume and number of seed points depend onthe information provided by clinical studies and literature regardingthe preferred or optimal openings and pore size per volume.

While the figures illustrate the disclosed methods using a cubical spaceor cubical spatial coordinates, it will be noted here that thisdisclosure is not limited to six-sided base structures or six-sidedouter geometries. Instead, as mentioned previously, the disclosedmethods apply to any space filling polyhedra (sometimes referred to asplesiohedra), space-filling convex polyhedra with regular facesincluding the triangular prism, hexagonal prism, cube, truncatedoctahedron and gyrobifastigium, space-filling convex polyhedra withirregular faces including the rhombic dodecahedron, elongateddodecahedron, and squashed dodecahedron, and any non-self-intersectingquadrilateral prism. Other possibilities are too numerous to mentionhere. In lieu of Cartesian coordinates, spherical, cylindrical and othercoordinates may also be used that would require the tiles to beappropriately scaled as they are positioned further away from the originbase tile. In a refinement, a gradient density algorithm can beincorporated into the data for the base tile to aid in matching up theborders between tiles. Thus, use of the terms “tile,” “volume,” and“initial geometry” herein covers multiple types of three-dimensionalshapes.

In the preferred embodiment, the base volume of randomized seed pointsmay then be multiplied and tiled together with other identical basevolumes to form a three dimensional scaffold for a porous structure,where the scaffold has a controlled randomness. However, in otherrefinements, a single base volume of randomized seed points can serve asthe scaffold for the porous structure. That is, if the initial volumeselected is sufficiently large, then it can serve as the scaffold of aporous structure after seed points are planted and randomized in acontrolled manner as described above. In this refinement, it may not benecessary to confirm compatibility with other identical volumes sinceonly one volume is necessary to form the scaffold. The methods of thepresent disclosure are applicable to fabricate a variety of implants,including but not limited to, implants of the hip, including compressionhip screws, knee, ankle, dental, shoulder, foot/hand, flanges, spine,skull plates, fracture plates, intramedullary rods, augments, staples,bone screws, cardiovascular implants, such as heart valves andartificial heart and ventricular assist devices, ligament and musclefasteners, other small joint implants, and other implants. Also, whilethe base volume of randomized seed points is preferably used to buildthree dimensional scaffold structures for porous implants, it may applyto other applications as well, such as manufactured items that requireresistance to vibrations, irregular loads, twisting of the structure,such as filters, heat sinks, cushions, wound dressings, cartilage or fatpad substitute, instrument weight reduction material, rasp, tissuesampling structure, debridement burr.

The disclosed techniques for fabricating porous structures of controlledrandomness substantially reduce memory requirements of the RMT. Forinstance, the calculation for an initial tile or volume can beduplicated and reused to build an implant or many implants.

In embodiments using a plurality of identical volumes of randomized seedpoints produced by the process described above, it is also desirable todefine an initial volume that is as large as possible so that the finalscaffold has a minimal number of seams between tiles or volumes. If aspherical, cylindrical, etc. coordinate system is chosen, the tiles arescaled as they are positioned further and further away from the originof the coordinate system or center of an array of seed points such asthe one shown in FIG. 9. In that case, a gradient density within unittiles may be used to aid in matching up the borders between tiles. Thetechniques for reducing memory and use of various software algorithmswould still apply. The data can be exported to a RMT machine directly orexported to a machine or computer that controls the RMT machine.

Also in refinements of scaffolds using a plurality of identical volumesof randomized seed points, struts are then created for the scaffold bydividing the space between the randomized seed points with lines aftercompatibility between the identical cubes or tiles or volumes isconfirmed. The division of the volume can be achieved in several ways.Preferably, it is done by applying any higher-order Voronoi tessellationalgorithm, such as a QHull algorithm, Ken Clarkson's “Hull” algorithm,cdd, or Mac-Queen's k-means algorithm, to the randomized seed points.However, any method/algorithm of calculating the three-dimensionalVoronoi tessellation, other than a QHull algorithm, may produceacceptable results. Because the compatibility between the identicalcubes or tiles or volumes of randomized seed points has been confirmed,the Voronoi tessellation algorithm can be applied before or after themultiplication of the base volume of randomized seed points. That is,one way the scaffold can be built is by (1) creating a base volume ofrandomized seed points according to the disclosed methods, (2)multiplying and tiling a sufficient number of identical base volume ofrandomized seed points to form a scaffold with the desired dimensions,(3) dividing the space between all the randomized seed points generatedby the copying and tiling of the base volumes, e.g., applying a higherorder Voronoi tessellation algorithm, to form the struts of thescaffold, and (4) removing the seed points to form a three dimensionalmodel of the randomized scaffold. A second way it can be done is by (1)creating a base volume of randomized seed points according to thedisclosed methods, (2) dividing the space between the randomized seedpoints of just that single base volume of randomized seed points, e.g.,applying a Voronoi tessellation algorithm, to form the struts for thatbase volume, (3) removing the seed points to form a base volume withrandomized struts, and (4) multiplying the base volume with randomizedstruts and tiling a sufficient number of identical base volumes withrandomized struts to form a scaffold with the desired dimensions. Bothof these ways of dividing the space between the randomized seed pointsresult in the same division and randomized struts structures for thescaffold. Also, before the space between the randomized seed points isdivided, it is contemplated that certain seed points may be eliminatedor additional seed points may be added to achieve the irregularityand/or porosity as desired or required by certain applications.

In one embodiment, a user can code the software program used to dividethe space between the seed points to eliminate any redundant lines. FIG.10 illustrates a base volume with randomized struts produced accordingto the present disclosure. That is, an initial geometry and volume wereselected, inner and outer seed points were distributed according to thedesired openings and pore size per volume, all or certain seed pointswere identified and randomized according to a predeterminedrandomization limit, the volume between the randomized seed points wasdivided according to an algorithm, e.g., Voronoi tessellation, and theseed points were removed to form tile or volume 1000 of FIG. 10. Volume1000 of randomized struts can be tiled or stacked to form a scaffold fora porous structure of desired dimensions. After the size and thicknessof the struts are selected, the scaffold model can be sent directly tothe RMT machine to fabricate the porous structure.

In other embodiments, however, the step of dividing the space betweenthe randomized seed points and eliminating any redundant lines may beseparated. Referring to FIG. 11, the triangulated base volume or volumeof randomized struts 1100 was produced by a different division of thespace between the seed points where the division yielded variousredundant lines or struts. FIG. also illustrates the spatial arrangementof the center tile to its coordinate neighbor tiles. The creation ofredundant lines is typical of many Voronoi tessellations and/or QHullalgorithms. If not eliminated, these redundant lines would result inunnecessary struts and nodes, which could consume unnecessary amounts ofmaterial and/or create various structural problems related to strength,porosity, connectivity, in the pore structure or incompatibilitiesbetween neighboring volumes with randomized struts.

One way of removing the excess redundant lines is illustrated in FIGS.12-13. In FIG. 12, a convex hull 1202 is illustrated, where the convexhull 1202 is one of many that is part of the base volume 1100 of FIG. 11before the redundant lines are removed. In FIG. 12, the structural lines1204 of the convex hull 1202 are shown as thinner lines and theredundant lines 1206 of the convex hull 1202 are shown as thicker lines.FIG. 13 illustrates the treatment of one area 1300 of the convex hull1202 to remove redundant lines 1206. Referring to FIG. 13, to eliminateor at least reduce the number of redundant lines 1206, a determinationis made as to the extent which an alleged redundant line 1206 and/or afacet 1210 created by one or two redundant lines 1206 is co-planar withthe surrounding structural face. Specifically, referring to FIG. 13,facets 1210 which may have redundant lines 1206 are identified. If anangle, between a line normal to a facet 1210, e.g., N₄, and a linenormal to neighboring facet 1210, e.g., N₃, is sufficiently small orbelow a threshold angle θ, then the shared redundant line or redundantlines 1206 between facets could be eliminated. Similarly, if a linenormal to the polygon face and a line normal to a facet 1210 issufficiently small or below a threshold angle θ, then the interiorredundant line or redundant lines 1206 may be eliminated. Otheralgorithms to eliminate redundant lines 1206 may be used. For instance,angles between lines can be compared with a threshold angle, andeliminated if they are less than the threshold angle. Alternatively, ashape recognition algorithm using polygon shape templates or polyhedralshape templates may be used to identify lines within the triangulatedtile 1100 that collectively approximate the shape of the template.Structural lines 1204 not forming a portion of or falling within atolerance of a shape template may be considered redundant lines 1206 andbe removed.

The threshold angle θ is typically 10° or less, e.g., 1°, 2°, 3°, 4°,5°, 6°, 7°, 8°, or 9°. If, after choosing a threshold angle θ that maybe too low and some of the openings in a convex hull 1202 are stillobscured by a number of redundant lines 1206, the threshold angle θ maybe increased and the algorithm re-run. However, choosing a highthreshold angle θ, e.g., greater than 10°, may risk of removing some ofthe desirable edges of a base volume with randomized struts. This isgenerally not desirable, but may advantageously be used to increase poresize without significantly affecting the strength. In anotherrefinement, the threshold angle range may be less than 6°, and morepreferably, the threshold angle range may be less than 4°.

The above-described threshold angle θ limitation technique can alsoyield a base volume with randomized struts similar to base volume 1100of FIG. 11. The base volume 1100 can be produced from the convex hull1202 of FIG. 12 using a threshold angle θ of less than 10°. As shown inFIGS. 14-15, the resulting base volumes 1100 (whether produced by a onestep Voronoi tessellation and redundant line removal or a two-stepalgorithms) fit together seamlessly with compatible faces 1502 and 1504.This is possible because the spatial coordinates (locating the voids) inclose proximity to the compatible faces on each tile were placed in acompatible arrangement before the web or scaffold of struts for eachtile was created. While the preferred embodiment provides for a porousstructure where the redundant lines are removed to eliminate all loosestruts, it is envisioned that other embodiments may have loose strutsand are still in accordance with the present disclosure.

After a scaffold comprising one or more base volumes of randomizedstruts is created, the line data of that scaffold may be exported amodeling program or algorithm, or directly to rapid manufacturingequipment (e.g., by first converting line data to a *.stl file anddownloading to a rapid prototyping machine). When the scaffold is sentdirectly to the machine, it must have a means of determining whichportion of the scaffold should be built and which should be ignoredbecause it is outside of the solid part. In one example, the linesdefining the struts of base volume 1100 may be assigned a coordinatesystem, which can be used to transform individual STL shellsrepresenting an idealized strut of appropriate shape and thickness tothe location of the lines. Then the resulting collection of STL shellsis written to an STL file to define a porous three-dimensional tile. Inanother example, the lines defining the struts of base volume 1100 maybe converted to a text file (*.exp extension) that corresponded toUNIGRAPHICS™ “expressions” that could be imported into such a modelingprogram. The solid-modeling program serves the purpose of taking ascaffold structure with infinitely thin lines, such as the base volume1100 of FIG. 11 and provides the struts with appropriate shapes andthicknesses T. FIG. 16 demonstrates examples of the different geometricshapes 1602 and thicknesses T available for the struts 1204, e.g.,circle, triangle, pentagon. The identified shapes are for demonstrationpurposes and are not intended to limit the scope of the claims orpresent invention. For example, other geometric shapes can include asquare, rectangle, hexagon, octagon, heptagon, etc. In some embodiments,the strut thickness can be proportional to the length of the strut orthe pore size. For instance, if the pores are bigger, they canaccommodate larger struts and still maintain a desired pore openingsize. Also, in instances where the struts are longer than apredetermined or selected length, they can be thickened to create moreuniform strength characteristics with struts that are shorter as longstruts are more flexible and/or weaker than shorter struts having thesame thickness.

In other refinements, the three dimensional scaffold model may beconverted to line data readable by a CAD program or directly to datareadable by a solid modeling program if not already in a format directlyreadable by rapid manufacturing equipment. Other sold-modeling programsmay be used or algorithms may be used to apply one or more predeterminedthicknesses to the line data of the three dimensional scaffold model, sothe model can be exported to the machine for fabricating a correspondingporous structure.

In one embodiment, during the modeling process, the strut lines 1204(e.g., FIG. 11, 14, or 15) may be recorded in a part file, and then whenreading in the lines 1204 using a modeling program and applying thedesired thicknesses T, the struts 1204 may be oriented to match anadjacent tile or volume. The locations of each endpoint of each strut1204 may be read as an ordered pair. The modeling program may also allowthe diameter/thickness of strut 1204 and any other relevant informationto be inputted, such as the general width, length, and height of thetile or volume 1100 (e.g., FIG. 11). Randomization algorithms similar tothose described herein for perturbing seed points may also be used torandomly assign cross-sectional shapes or randomly assign strutthicknesses to one or more lines 1204 in any portion of the base volumeof randomized struts 1100 of FIG. 11. Asymmetries or non-uniformprofiles may be defined in a part file and then associated with one ormore lines 1204 to form one or more struts within a tile or volume,e.g., volume 1100 of FIG. 11, that are non-uniform. Such associationsmay be random, selectively predetermined, or may be applied to everyline within a base volume of randomized struts. Struts 1204 may also berandomly or non-randomly assigned a taper angle or a varyingcross-sectional shape from one endpoint to another endpoint. Providingdifferent shapes and/or dimensions to each strut as described mayprovide better strength, biologic fixation, and trabecular appearance,while maintaining full control of overall porosity.

In at least the refinements where the volume of randomized seed pointsare first multiplied and tiled to form a generally shaped scaffold ofdesired dimensions before the total volume of that scaffold is dividedbetween the randomized seed points, an algorithm to unite the differentvolumes may not be necessary as process produces a seamlessly dividedoverall scaffold. In other refinements, however, a Boolean unitealgorithm may be used to create a more unified scaffold if necessary.Referring to FIGS. 17-19, after one of the tiles 1702, 1802, 1902 iscreated, the data for the lines 1204 of the volume 1100 (e.g. FIG. 11)are no longer needed and may be deleted to keep the file size to aminimum. In one variation, the file may be save as a *.prt, or partfile, which is the native file format for UNIGRAPHICS™. A para-solidformat may also be employed.

In FIG. 17, individual tiles 1702 have struts that have been randomizedat a 10% randomization limit. Porous structure 1700 is made up of fouridentical tiles 1702. Similarly, in FIGS. 18 and 19, tiles 1802 havestruts randomized at a 20% randomization limit and tiles 1902 at a 30%randomization limit. While FIGS. 17-19 show porous structures 1700,1800, and 1900 comprising identical tile volumes, these serve asexamples and do not limit the scope of the invention. For instance, inone embodiment, a porous structure can comprise of a combination oftiles that were randomized at limits of 0%, 10%, 20%, 30%, etc. In otherrefinements, a porous structure can comprise of tiles that havedifferent shapes, and the tiles may or may not have the samerandomization limits.

The tiles 1702, 1802, and 1902 may be arranged row by row and stackedwith only the outermost struts 1204 overlapping to create any size orshape as illustrated in FIGS. 17-19. The tiles or volumes 1702, 1802,and 1902 may be assembled to create a bulk structure for use at a latertime. A Boolean unite algorithm may be used to create the seamless bodyfrom two tiles 2002 and 2004 as shown in FIG. 20. As seen, tiles 2002and 2004 can be substantially identical or tiles 2002 and 2004 can bedifferent shapes and randomization. For example, FIGS. 28A and 28Billustrate an example of a porous structure having two tiles withdifferent maximum pore size. Regardless of the shape or randomization ofthe tiles, the disclosed methods provide for a seamless interfacebetween the porous tiles. Individual tiles can be exported as a filethat can be tiled within a rapid manufacturing machine or software usedby such machines. Individual tiles can be interpreted by the machine andthen mapped to individual 3-D tiled positions to minimize file size. Aswill be apparent to those skilled in the art, the 3-D tiles do not haveto be laid in a side-by-side fashion as illustrated in FIGS. 17-19. Asdiscussed above, machines may include metal ‘selective’ laser sinteringmachines (SLS), electron beam melting machines (EBM), or laserengineered net shaping (LENS™) machines.

Also, many software applications will work to perform the tiling/formingoperation. The tiling can be performed in a solid-modeling program likeUNIGRAPHICS™, in a program used for advanced NURBS™ and triangulationmanipulation such as GEOMAGIC™, in a program dedicated to triangulatedfile formats like NetFabb, or manually in the *.stl file itself *.stlfiles are simply a representation of triangulated solids which can betranslated and mirrored with any number of bodies. Once the solid hasbeen tiled and manipulated as desired, an *.stl file or the like can beused in rapid-prototype machines. Once the desired structure is defined,it can be exported to a format readable by rapid prototype machines suchas *.stl (stereolithography) format. While the specific tiles 1802,1902, and 2002 disclosed FIGS. 18-20 are rectangular and arrayedaccordingly, the disclosed methods apply to a multitude of tilingpatterns in three dimensions, such as spherical and cylindricalcoordinate tilings. The disclosed methods would be applicable toacetabular cups and stems for example.

Scanning Electron Microscopy (SEM) photographs of a portion of tiles1702, 1802, 1902 disclosed FIGS. 17-19 are shown in FIGS. 21-22, andconventional enlarged photographs of tiles 1702, 1802, 1902 disclosedFIGS. 18-20 are shown in FIGS. 23-25. FIG. 24 is a photograph of acurved portion of a metaphyseal cone fabricated on an EOS™ metal lasersintering machine, employing random struts and a 30% randomizationlimit. FIG. 23 is a photograph of a top portion of the metaphyseal coneshown in FIG. 23. FIG. 25 is a photograph of a cone section of ametaphyseal cone shown in FIGS. 23-24.

Preferred embodiments of porous structures may include 60-85% porosityas known to those skilled in the art. In some embodiments, the averagediameter of the pores of the present invention is in the range of 0.01to 2000 microns. More preferably, the average diameter of the pores isin the range of 50 to 1000 microns. Most preferably, the averagediameter of the pores is in the range of 400 to 850 microns. FIG. 21illustrates one exemplary way the average pore diameter may be measured.The average pore diameter typically is measured by the average diameterof the larger openings captured by an SEM image. In other embodiments,the average diameter 2102 may be measured horizontally or at any desireddiagonally position. The average diameter of smaller openings or windowsmay also be measured.

In a refinement, the average strut thickness for a tile ranges fromabout 100 μm to about 400 μM. More preferably, the range is from about180 μm to about 300 μm. In another refinement, the average pore size(MVIL) or fenestration opening diameter ranges from about 200 μm toabout 1970 μm, more preferably from 100 μm to 700 μM, and mostpreferably from 200 μm to 450 μm. Also, the strut thicknesses may berandomized and/or the pore sizes may be randomized.

MVIL refers to Mean Void Intercept Length, which is another way ofcharacterizing the average pore size, particularly in structures wherethe pore shapes and sizes are not uniform. One generally knowndefinition of MVIL is “measurement grid lines are oriented parallel tothe substrate interface. The number of times the lines intercept voidsis used with the volume percent void to calculate the mean voidintercept length.”

Boolean-intersect and Boolean unite functions may be employed with basevolume of randomized struts 1100 (e.g., FIG. 11) or tile structures likethose shown at 1702, 1802, and 1902 disclosed FIGS. 17-19 to apply acoating 2602 on a surface 2604 of an implant or substrate 2606 asillustrated in FIGS. 26A-26C, and the data can be exported to thefabrication machine either with the substrate 2606 data or separately.In FIGS. 26A-26C, the substrate 2606 is a tibial tray that is coatedwith a plurality of tiles 2702 shown in FIG. 27 to form a porouscoating. The desired thickness of the Boolean intersect volume of thecoating 2602 is shown at 2704 in FIG. 27. The volume and shape 2610 ofthe porous material shown in FIG. 26A is used in a Boolean intersectalgorithm to convert the larger tile 2702 shown in FIG. 27 to a smallerportion 2612 shown in FIG. 26B for filling the Boolean intersect volume2610 of FIG. 26A. Thus, using the Boolean intersect algorithm, less thanthe entire tile 2702 of FIG. 27 may be used to form the portion 2612 ofthe desired coating geometry or Boolean intersect volume 2610 to createa desired shape. As shown in FIG. 26C, a Boolean unite function may beused to unite the portion 2612 of porous material with surroundingmaterial as the actual coating 2602 is being constructed. Alternately,all of the tiles 1100 (e.g., FIG. 11) or tile structures could be joinedtogether using a Boolean unite and then intersect the joined tiles allat once with the portion 2612 in sub-sections or as a whole. It shouldbe noted that while not shown in the drawings, a base volume ofrandomized struts, e.g., 1100, may be used to create the portion to bejoined 2612, instead of a tile 2702. This may be done such that Booleanintersect volume 2610 is filled with portions of united or un-unitedportions 2612 of base volume 1100. Strut thicknesses T may be assignedto one or more of the lines 1204 of the tile portions 2612 before orafter uniting them. Alternatively, strut thicknesses T may be assignedto one or more of the lines 1204 after the tile portions 2612 areindividually or collectively intersected with substrate 2606. Inalternative embodiments, Boolean difference or trim operations usingplanes or sheets can also be used to create the desired shapes, such asvolume 2610. In another refinement, before strut thicknesses T may beassigned, a Boolean trim may be performed on the lines 1204 to eliminatecertain portions of the lines 1204. As discussed, alternate methods ofpartitioning the porous volume into its final shape may encompasscombinations of intersecting and shaping the solid or precursor linesusing trimming sheets. Alternately, this shaping or partitioning bytrimming sheets may be performed after slicing or interpreting the solidand porous material into a format readable by a rapid-manufacturingmachine.

As mentioned above, FIG. 28A illustrates porous structure 2800 havingtwo tiles 2802 and 2804 joined together seamlessly according to thepresent disclosure. FIG. 28B is a blown up partial view of the seamlessinterface between tile 2802 and tile 2804. As demonstrated by FIGS.28A-28B, the tiles 2802 and 2804 have been designed with a peripherythat matches seamlessly on all sides. That is, any permutation ofarranging a plurality tiles 2802 and 2804 would result in a porousstructure that does not have any discernable seams between the tiles.For example, the interfaces would be seamless between an arrangementhaving all tiles 2802, or all tiles 2804, or any combination thereof.Yet the inner struts of tile 2802 differ from the struts of tile 2804.For example, tile 2802 has fewer, and therefore, larger pores than tile2804. The seamless interface was created without the need to manuallymanipulate the struts to match up or to perform any node matchingalgorithm.

As demonstrated, the present disclosure provides for the seamlessinterface between two different scaffold unit tiles without the need tomanually manipulate the struts of the two tiles to match up to oneanother. Instead, in some embodiments, the seamless interface wascreated by manipulating the negative space, i.e., the space between thestruts. The negative space manipulation can be achieved by ensuring thatthe seed points at the interface between the two tiles, whethersubstantially identical in shape and randomization or substantiallydifferent, correspond to one another. For instance, preferably, thereshould be only one shared subset of outer seed points at the interfaceof two tiles. This can be achieved at least by randomizing the outerseed points separate from the inner seed points, limiting therandomization of certain inner seed points, or adding or removing innerseed points. After the negative space is divided to form a scaffold,then the struts can be given a shape and a size to create a seamlessporous structure that is made up of different tiles. Preferably, twoseed point clouds, whether dissimilar or not, that share a boundarybefore the scaffold is created will share struts after the scaffold iscreated.

In view of the above, the present disclosure provides for methods tofabricate a randomized porous structure by manipulating the negativespace, i.e., the space between the struts, rather than manipulating thestruts themselves for randomization. Accordingly, the methods of thepresent disclosure allows for time- and cost-effective fabrications ofcomplex porous structure. The present disclosure provides for methods tofabricate original randomized structures, as opposed to a randomizedexisting structure, that have seamless unions between any connectingunits. Consequently, the porous structure created according to theaspects of the present disclosure provide improved strength withoutrequiring the struts to be thicker, as other uniform porous structuresmay. Further, the randomized structure provides enhanced stress orvibration resistance due to the randomized placement of the struts andtheir intersections, thereby eliminating planes of fractures that existin uniform structures where the structures are exposed to shear stress.Additionally, the improved complexity of the porous structures of thepresent disclosure provides for resemblance of trabecular features andimproved porosity. Moreover, the methods of the present disclosure allowfor simple and efficient customization of a porous structures with thedesired strength, pore distribution, average pore sizes, porosity, etc.

Also, the present disclosure may be used to create and combine aplurality of tiles without randomizing the seed points. The tiles canhave substantially identical or substantially different shapes and/orsizes, ranging from simple to complex structure, as long as the tileshave the same or corresponding outer seed points, a seamless interfacecan be formed when the space is divided. In some embodiments, creating aseamless union between one tile of one shape or size can have a regulardistribution of seed points and another tile of another shape and/orsize can be done by ensuring the same placement in both tiles of theseed points that most influences the boundary between the tiles, i.e.,the outer seed points. For example, it is difficult to create aWeaire-Phelan structure as a tile that is stackable to form a seamlessporous structure. The methods described in the present disclosure,however, provide for simple techniques to achieve such tasks and allowfor automation of such process via programming of software.

Although the present invention and its advantages have been described indetail, it should be understood that various changes, substitutions andalterations can be made herein without departing from the spirit andscope of the invention as defined by the appended claims. Moreover, thescope of the present application is not intended to be limited to theparticular embodiments of the process, machine, manufacture, compositionof matter, means, methods and steps described in the specification. Asone of ordinary skill in the art will readily appreciate from thedisclosure of the present invention, processes, machines, manufacture,compositions of matter, means, methods, or steps, presently existing orlater to be developed that perform substantially the same function orachieve substantially the same result as the corresponding embodimentsdescribed herein may be utilized according to the present invention.Accordingly, the appended claims are intended to include within theirscope such processes, machines, manufacture, compositions of matter,means, methods, or steps.

1. A model of a three-dimensional structure for use by a computer-aidedmanufacturing apparatus, comprising: a porous geometry having an outerboundary, the porous geometry composed of a plurality of struts, eachstrut connected to one or more other struts at a node; wherein eachstrut has an elongated body and a node at each end thereof; and whereineach node lies on the interior of the porous geometry or on the outerboundary of the porous geometry of the three-dimensional structure. 2.The model of claim 1, wherein the model is created by a methodcomprising: populating a volume encompassing the porous geometry with aplurality of unit volumes, wherein some of the unit volumes contain allor a portion of the outer boundary of the porous geometry.
 3. The modelof claim 2, the method further comprising: defining one or more seedpoints on the outer boundary, the one or more seed points defininglocations of one or more of the struts of the porous geometry thatintersect the outer boundary, each of the struts intersecting the outerboundary having two nodes on the outer boundary, one node outside on theouter boundary and one node in an interior of one of the unit volumes,or one node on the outer boundary and one node in an interior of one ofthe unit volumes.
 4. The model of claim 3, the method furthercomprising: moving some or all of the seed points to a new location. 5.The model of claim 4, wherein some or all of the defined seed points aremoved to new locations such that struts defined by the moved seed pointshave an end node on the outer boundary.
 6. The model of claim 4, whereinthe new locations to which the seed points are moved are a randomdistance and a random direction from an original location of the seedpoint.
 7. The model of claim 4, wherein moving some of all of the seedpoints causes some of the seed points to be moved to a new location thatcauses an end node of one or more struts to be located outside of theouter boundary.
 8. The model of claim 4, wherein moving some of all ofthe of the seed points causes a change in length of one or more strutswhose positions are defined by the new locations of the one or morerepositioned seed points.
 9. The model of claim 4, wherein struts havinga node outside of the outer boundary caused by movement of a seed pointare discarded.
 10. The model of claim 4, wherein movement of a seedpoint that causes a node of a strut to be outside of the outer boundarycauses the portion of the strut outside of the outer boundary to bediscarded.
 11. The model of claim 10, wherein movement of a seed pointthat causes an end node of a strut to be outside of the outer boundaryfurther causes a new node for the strut to be defined on the outerboundary.
 12. The model of claim 4, wherein struts having a node outsideof the outer boundary caused by movement of a seed point are retained inthe model.
 13. The model of claim 2, wherein the unit volumes aresubstantially identical.
 14. The model of claim 2, wherein the outerboundary of the porous geometry is defined by edges or sides of some ofthe unit volumes.
 15. The model of claim 1, wherein the model is savedto a computer-readable file suitable for use by a computer-aidedapparatus for building the three-dimensional structure.
 16. A processfor fabricating a three-dimensional structure from a model using acomputer-aided apparatus comprising: taking as input the model of thethree-dimensional structure; and controlling the energy source tofabricate the three-dimensional structure; wherein the model of thethree-dimensional structure comprises: a porous geometry having an outerboundary, the porous geometry composed of a plurality of struts, eachstrut connected to one or more other struts at a node; wherein eachstrut has an elongated body and a node at each end thereof; and whereineach node lies on the interior of the porous geometry or on the outerboundary of the porous geometry of the three-dimensional structure. 17.The process of claim 16, wherein the computer-aided apparatus comprises:a build platform; a processor; an energy source; and software forexecution on the processor for controlling the energy source.
 18. Theprocess of claim 17, wherein fabrication of the three-dimensionalstructure uses an additive fabrication technique to construct thethree-dimensional structure, the technique comprising: iterativelydepositing successive layers of a material onto a substrate; and fusing,melting, re-melting or sintering each successive layer of material;wherein each successive layer of material is fused, melted, re-melted,or sintered by application of energy from the energy source to portionsof the powder layer corresponding to a cross-section of thethree-dimensional structure, under control of the software.
 19. Theprocess of claim 18, wherein the material is metal powder.
 20. Theprocess of claim 18, wherein the energy source is a laser providinglaser energy.
 21. An orthopedic implant comprising an implant structuremanufactured in accordance with a computer-aided design modelcomprising: a porous geometry having an outer boundary, the porousgeometry composed of a plurality of struts, each strut connected to oneor more other struts at a node; wherein each strut has an elongated bodyand a node at each end thereof; and wherein each node lies on theinterior of the porous geometry or on the outer boundary of the porousgeometry of the three-dimensional structure.
 22. The orthopedic implantof claim 21, the model created by a method comprising the steps of:populating a volume encompassing the porous geometry with a plurality ofunit volumes, wherein some of the unit volumes contain all or a portionof the outer boundary of the porous geometry; defining one or more seedpoints on the outer boundary, the one or more seed points defininglocations of one or more of the struts of the porous geometry thatintersect the outer boundary, each of the struts intersecting the outerboundary having two nodes on the outer boundary, one node outside on theouter boundary and one node in an interior of one of the unit volumes,or one node on the outer boundary and one node in an interior of one ofthe unit volumes; and moving some or all of the seed points to a newlocation.